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navik [9.2K]
3 years ago
10

The standard formula for the volume of a cone is V=πr2h3. If the cone is scaled proportionally by a factor of k, its volume beco

mes V' = V × k3. Use your algebra skills to derive the steps that lead from V=πr2h3to V' = V × k3 for a scaled cone.

Mathematics
2 answers:
DaniilM [7]3 years ago
8 0

The volume of a cone with base radius <em>r </em>and height <em>h</em> is

V = \frac 1 3 \pi r^2 h

What happens when we scale by <em>k </em>?

Let <em>V'</em> be the volume of a cone with radius <em>rk</em> and height <em>hk</em>

V' = \frac 1 3 \pi (rk)^2 (hk) = \frac 1 3 \pi r^2 k^2 h k = k^3 (\frac 1 3 \pi r^2 h) = k^3 V

ANEK [815]3 years ago
3 0

Answer:

Step-by-step explanation:

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